△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ?
Accepted Solution
A:
Let b1-------------> base △ABC b2-------------> base △DEF A1-----------> area △ABC A2-----------> area △DEF
we know that h1=20 in h2=24 in A1=b1*20/2-------------> A1=10b1 A2=b2*24/2 ------------> A2=12 b2
if △ABC∼△DEF then b1/20=b2/24------------> b1=b2*[20/24]-----> b1=b2*[5/6]
What is the ratio of the area of △ABC to the area of △DEF? A1=10b1 A2=12b2 A1/A2=(10/12)*(b1/b2)-------> (10/12)*(b2*(5/6)/b2)-----> (10/12)*(5/6)=50/72